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%I #7 Apr 11 2013 13:31:20
%S 1,1,-1,2,-3,1,6,-11,6,-1,30,-61,41,-11,1,240,-518,389,-129,19,-1,
%T 3120,-6974,5575,-2066,376,-32,1,65520,-149574,124049,-48961,9962,
%U -1048,53,-1,2227680,-5151036,4367240,-1788723,387669,-45594,2850,-87,1
%N Triangle, read by rows: T(0,0) = 1, T(n,k) = F(n+1)*T(n-1,k) - T(n-1,k-1) where F(n+1) is the (n+1)st Fibonacci number.
%C For n>0, the row sums are 0. For n>1, sum(k=0..n) 2^k*T(n,k) = 0. The first subdiagonal (1,-3,6,-11,19,...) is an alternating signed version of A001911 (Fibonacci numbers - 2). The first row is A003266 (product of Fibonacci numbers).
%e Triangle begins
%e 1;
%e 1, -1;
%e 2, -3, 1;
%e 6, -11, 6, -1;
%K sign,tabl
%O 0,4
%A _Gerald McGarvey_, May 26 2005
%E Corrected a sign in the definition. - _N. J. A. Sloane_, Apr 11 2013